Spares Provisioning for Repairable Items: Cyclic Queues in Light Traffic

The classic machine repair problem is extended and modeled as a cyclic queue for the purpose of determining the number of spares and repair channels for a population of items subject to stochastic failure. In this system the operating units, removal of failed units, transportation to repair depot, and the repair itself are treated as four multi-server stations, each with exponential holding times. An exact model is developed from the literature on networks and cyclic queues and compared with a series approximation. Under a constraint requiring a high availability of spares which insures “light traffic queues,” the approximate model is found to be very accurate and computationally more efficient.